Addition of Algebraic Fractions: Monic Denominators

Transcript

You can see we want to add two different fractions. Now what I’m going to do before adding or doing anything, always as we usual, factorize! So see how here we can see that x is common factor and here x is also a common factor, so we’ll take those common factors out like that. So here it will be x x minus 2 and here it will be x x plus 4.

And now you can see what’s common? x is common, isn’t it? So we don’t have to worry much about x but to make in order to make a common denominator, we have x common, we have x minus 2 here but we don’t have an x plus 4. We have x plus 4 here but we don’t have x minus 2. So what I’m going to do is multiply the top and bottom by the factor that they don’t have. That each of the fractions don’t have. So see how in this fraction, we don’t have x plus 4. So I’m going to multiply x plus 4 to both top and numerator, okay?

So make sure when you do something to the top you do something to the bottom as well. You’ve got to do the exact same thing to the bottom. And here, we don’t have x minus 2, so I’m going to multiply both top and bottom by x minus 2.
And now you can see that one times x plus 4 is x plus 4 and now the denominator is x x minus 2, x plus 4, and same with this side x x plus 4, x minus 2 which is the same, isn’t it? Yeah because now we have the same denominator.

We can go ahead and add the numerators, so it’s going to be just 2x plus 2 because x plus x is 2x, 4 minus 2 is 2. So that’s how we merge those two fractions together and make sure you leave the denominator the same, okay? So the denominator must be the common denominator. So you don’t have to change anything with the denominators for the last answer, okay? That’s the idea, guys! You should be used to this. It shouldn’t be too new. Okay, let’s factorize! Now guys I won’t go through all the cross methods anymore. You guys should be pretty quick at this now. So let’s try do it quickly as well. So here’s 15. 15, the factors of 5 and 3, so 5 plus 3 is 8.

So that’s what I’m going to do x plus 3, x plus 5, okay? And here’s 30. What should we use? We could use 6 and 5, 3 and 10, but I might use 6 and 5 because I know that 6 plus 5 is 11. So I’m going to use x plus 5, x plus 6, okay? Now again, compare the denominators. We’ve got x plus 5 which is common but this fraction, we don’t have x plus 6, and this fraction, we don’t have x plus 3. That’s what you’re going to multiply top and bottom by. So here, I’m going to multiply the top and bottom by x plus 6 because that’s what we don’t have. And here, x plus 3 on top and bottom, okay?

And then multiply them together, so 1 times that is that 1 times that is that, and you can see how the denominator, it’s x plus 3, x plus 5, x plus 6, and same over here, it’s the same thing, okay? So now we can add the numerators. So x plus x is 2x, 6 plus 3 is 9 over the same denominator, okay?